Year: 2012
International Journal of Numerical Analysis and Modeling, Vol. 9 (2012), Iss. 4 : pp. 970–981
Abstract
In this paper, we consider the problem of computing numerical solutions for stochastic differential equations (SDEs) of Itô form. A fully explicit method, the split-step forward Milstein (SSFM) method, is constructed for solving SDEs. It is proved that the SSFM method is convergent with strong order $\gamma=1$ in the mean-square sense. The analysis of stability shows that the mean-square stability properties of the method proposed in this paper are an improvement on the mean-square stability properties of the Milstein method and three stage Milstein methods.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2012-IJNAM-668
International Journal of Numerical Analysis and Modeling, Vol. 9 (2012), Iss. 4 : pp. 970–981
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Stochastic differential equation Explicit method Mean convergence Mean square convergence Stability Numerical experiment.